Each arm will consist of low-risk TBI patients (defined as patients with a subdural or epidural hematoma < 8mm, intraparenchymal contusion < 2 cm, and/or single contusion per lobe) who have had a CT scan of the head without contrast at 24 hours post-injury which documents a stable injury pattern. The severity of neurologic deficit will have no bearing on their suitability for participation, and will not be considered in inclusion/exclusion criteria. After documentation of a stable intracranial injury pattern at this time interval, patients will be randomized to receive either enoxaparin 30 mg SQ every 12 hours or placebo with each regimen being initiated at 24 hours post-injury. A follow-up CT scan of the brain without contrast will be obtained on all patients 48 hours post-injury (and 24 hours after the initiation of enoxaparin/placebo). An additional CT scan of the brain without contrast will be obtained on any patient who experiences an abrupt change in neurologic exam at any time between the initiation of enoxaparin/placebo and the end of the study's interventional period at 96 hours post-injury (this time frame was chosen as it is the earliest time point at which there is universal agreement among both of our group's practitioners that enoxaparin use is safe from the risks of TBI expansion). Any patient with a worsened CT scan will have their investigational treatment discontinued at that time. At 96 hours post-injury, the interventional portion of the study will end, data collection for the primary endpoint will cease, and all patients will be placed on enoxaparin for the remainder of their hospital stay as per local standards of care. Patient participation in the study will last from the time of injury to 96 hours post-injury for the interventional part of the study, and from 96 hours post-injury until discharge from ETMC for the observational portion. While this latter time frame is obviously extremely variable, it averages approximately one to two weeks. During both the interventional and observational time periods, patients will have Duplex ultrasonography of the lower extremities performed for an edematous extremity, CT-angiography of the chest for unexplained hypoxia or tachycardia, and ventilation-perfusion scanning for suspicion of PE in the presence of a contraindication to IV contrast.